1. Technical Field
The present invention relates in general to the field of digital music synthesizers and in particular to a method and apparatus for selectively reducing the upper harmonic content of digital synthesizer excitation signals. Still more particularly, the present invention relates to a method and apparatus for selectively converting a sawtooth waveform to a triangle waveform in response to an increase in the frequency of the sawtooth waveform.
2. Description of the Related Art
Musical synthesizers have been well known in the prior art for some time. Early analog synthesizers typically utilized an excitation waveform generator capable of generating a sawtooth waveform, a triangle waveform and a square wave. The output frequency of the excitation waveform generator was controllable in response to the desired pitch and often a low frequency oscillator was connected to the excitation waveform generator to permit vibrato effects to be generated.
In such systems, the selectable output of the excitation waveform generator was then typically coupled to a filter and amplifier before being connected to an audio output device, such as a speaker.
Early researchers in the music synthesizer area discovered that the control of a suitable filter and voltage controlled amplifier may be expeditiously accomplished by means of a so-called Attack-Decay-Sustain-Release (ADSR) circuit. By selectively controlling the output of the ADSR circuit in each of its four segments, the excitation signal may be shaped and filtered to approximate the sound of the desired musical instrument.
In digital music synthesizer systems which utilize subtractive synthesis, a sawtooth waveform is typically utilized as the excitation signal. This is preferred due to the fact that a sawtooth waveform may be simply and easily generated in a digital system by the initiation of a signal, the incrementing of that signal by a constant value and the storing of the new value. This technique typically requires only three processor steps to accomplish. Additionally, a sawtooth waveform is an excellent selection for an excitation signal due to the rich harmonic nature of such waveforms.
One problem which exists with the utilization of a sawtooth waveform as an excitation signal for a digital music synthesizer occurs as a result of the rich high harmonic content of a sawtooth waveform. An aliasing problem, as will be described in greater detail below, creates a problem when attempting to synthesize high frequency sounds. Higher sampling rates may minimize the effect of this aliasing; however, in any attempt to implement a digital synthesizer utilizing a single digital signal processor a limited number of process steps are available for each note. Thus, the sample rate utilized in such systems is generally on the order of twenty to fifty thousand samples per second.
As those skilled in the digital signal processing art will appreciate, with a sampling rate of 20,000 samples per second the maximum frequency present in the resultant system is 10,000 cycles per second, as a result of the rule stated in the Nyquist Theorem.
As a result, as higher frequencies are synthesized utilizing a digital sample data system with a low sampling rate an aliasing problem will occur at those higher frequencies as the Nyquist frequency is approached due to a "folding over" which occurs at those frequencies. This aliasing problem may be masked by the utilization of a low pass filter to remove the upper harmonic content of the sawtooth waveform excitation signal; however, this approach cannot cure the aliasing problem and low pass filters are difficult to implement in a digital system and require a substantial amount of the available processor assets.
Thus, it should be apparent that a need exists for a method and apparatus whereby the upper harmonic content of a sawtooth waveform excitation signal may be minimized without requiring the utilization of extensive processor assets.